If a npn transistor is known to be in active mode the following equations will always hold true for it:

• ic = Is*exp(Vbe/Vt)
• ic = B*ib
• ic = ie - ib
• B = ic/ib
• a = B/(B+1)
• ie = ic + ib
• ie = Is*exp(Vbe/Vt) + ib
• ie = B*ib + ib
• ie = ib(B + 1)
• Vbe = vb - Ve
• Vce = Vc - Ve

Terms

• B, Beta is a manufacturing constant
• Vt, is the thermanl voltage typically around 25mV, but one shouldnt assume so unless you have to
• Vbe, is typically around .7v, but one shouldnt assume so unless you have to.

Derivations

Conculsions

Given Beta and one current nearly any piece of relevant information can be found.